Speaker：Weiyong He(University of Oregon)
Time：7：50-9：20, November 27, 2020
Room：Tencent Meeting: 950 391 9321,Password:112358 & 5405，the fifth teaching building
Harmonic almost complex structures was introduced by C. Wood in 1990s. We study the existence and regularity of weak harmonic almost complex structure from analytic point of view, as a tensor-valued version of harmonic maps. We introduce the notion of biharmonic almost complex structures, in particular in dimension four. We prove that biharmonic almost complex structures are smooth, and there always exist an energy-minimizing biharmonic almost complex structure. Moreover, given a homotopy class, we prove existence results which depends on whether M is spin or not. We also propose a conjecture that the homotopy class of energy-minimizing biharmonic almost complex structures do not depend on a generic background metric.
